6 Examples using Frobenius series on first order ode

6.1 Example 1. \(xy^{\prime }+y=0\)
6.2 Example 2. \(xy^{\prime }+y=x\)
6.3 Example 3. \(xy^{\prime }+y=1\)
6.4 Example 4. \(xy^{\prime }+y=k\)
6.5 Example 5. \(xy^{\prime }+y=\sin x\)
6.6 Example 6. \(xy^{\prime }+y=x+x^{3}+2x^{4}\)
6.7 Example 7. \(xy^{\prime }+y=\frac {1}{x}\)
6.8 Example 9. \(xy^{\prime }+y=\frac {1}{x^{2}}\)
6.9 Example 10. \(xy^{\prime }+y=3+x\)
6.10 Example 11. \(xy^{\prime }+y=\frac {1}{x^{3}}\)
6.11 Example 11. \(y^{\prime }+xy=x^{2}\)